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src/secp256k1/src/field_10x26_impl.h
/*********************************************************************** | /*********************************************************************** | ||||
* Copyright (c) 2013, 2014 Pieter Wuille * | * Copyright (c) 2013, 2014 Pieter Wuille * | ||||
* Distributed under the MIT software license, see the accompanying * | * Distributed under the MIT software license, see the accompanying * | ||||
* file COPYING or https://www.opensource.org/licenses/mit-license.php.* | * file COPYING or https://www.opensource.org/licenses/mit-license.php.* | ||||
***********************************************************************/ | ***********************************************************************/ | ||||
#ifndef SECP256K1_FIELD_REPR_IMPL_H | #ifndef SECP256K1_FIELD_REPR_IMPL_H | ||||
#define SECP256K1_FIELD_REPR_IMPL_H | #define SECP256K1_FIELD_REPR_IMPL_H | ||||
#include "util.h" | #include "util.h" | ||||
#include "field.h" | #include "field.h" | ||||
#include "modinv32_impl.h" | |||||
#ifdef VERIFY | #ifdef VERIFY | ||||
static void secp256k1_fe_verify(const secp256k1_fe *a) { | static void secp256k1_fe_verify(const secp256k1_fe *a) { | ||||
const uint32_t *d = a->n; | const uint32_t *d = a->n; | ||||
int m = a->normalized ? 1 : 2 * a->magnitude, r = 1; | int m = a->normalized ? 1 : 2 * a->magnitude, r = 1; | ||||
r &= (d[0] <= 0x3FFFFFFUL * m); | r &= (d[0] <= 0x3FFFFFFUL * m); | ||||
r &= (d[1] <= 0x3FFFFFFUL * m); | r &= (d[1] <= 0x3FFFFFFUL * m); | ||||
r &= (d[2] <= 0x3FFFFFFUL * m); | r &= (d[2] <= 0x3FFFFFFUL * m); | ||||
▲ Show 20 Lines • Show All 1,139 Lines • ▼ Show 20 Lines | static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) { | ||||
r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL); | r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL); | ||||
r->n[9] = a->n[7] >> 10; | r->n[9] = a->n[7] >> 10; | ||||
#ifdef VERIFY | #ifdef VERIFY | ||||
r->magnitude = 1; | r->magnitude = 1; | ||||
r->normalized = 1; | r->normalized = 1; | ||||
#endif | #endif | ||||
} | } | ||||
static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) { | static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a) { | ||||
secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1; | const uint32_t M26 = UINT32_MAX >> 6; | ||||
int j; | const uint32_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4], | ||||
a5 = a->v[5], a6 = a->v[6], a7 = a->v[7], a8 = a->v[8]; | |||||
/** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in | |||||
* { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: | |||||
* [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223] | |||||
*/ | |||||
secp256k1_fe_sqr(&x2, a); | |||||
secp256k1_fe_mul(&x2, &x2, a); | |||||
secp256k1_fe_sqr(&x3, &x2); | |||||
secp256k1_fe_mul(&x3, &x3, a); | |||||
x6 = x3; | |||||
for (j=0; j<3; j++) { | |||||
secp256k1_fe_sqr(&x6, &x6); | |||||
} | |||||
secp256k1_fe_mul(&x6, &x6, &x3); | |||||
x9 = x6; | |||||
for (j=0; j<3; j++) { | |||||
secp256k1_fe_sqr(&x9, &x9); | |||||
} | |||||
secp256k1_fe_mul(&x9, &x9, &x3); | |||||
x11 = x9; | |||||
for (j=0; j<2; j++) { | |||||
secp256k1_fe_sqr(&x11, &x11); | |||||
} | |||||
secp256k1_fe_mul(&x11, &x11, &x2); | |||||
x22 = x11; | |||||
for (j=0; j<11; j++) { | |||||
secp256k1_fe_sqr(&x22, &x22); | |||||
} | |||||
secp256k1_fe_mul(&x22, &x22, &x11); | |||||
x44 = x22; | /* The output from secp256k1_modinv32{_var} should be normalized to range [0,modulus), and | ||||
for (j=0; j<22; j++) { | * have limbs in [0,2^30). The modulus is < 2^256, so the top limb must be below 2^(256-30*8). | ||||
secp256k1_fe_sqr(&x44, &x44); | */ | ||||
} | VERIFY_CHECK(a0 >> 30 == 0); | ||||
secp256k1_fe_mul(&x44, &x44, &x22); | VERIFY_CHECK(a1 >> 30 == 0); | ||||
VERIFY_CHECK(a2 >> 30 == 0); | |||||
VERIFY_CHECK(a3 >> 30 == 0); | |||||
VERIFY_CHECK(a4 >> 30 == 0); | |||||
VERIFY_CHECK(a5 >> 30 == 0); | |||||
VERIFY_CHECK(a6 >> 30 == 0); | |||||
VERIFY_CHECK(a7 >> 30 == 0); | |||||
VERIFY_CHECK(a8 >> 16 == 0); | |||||
r->n[0] = a0 & M26; | |||||
r->n[1] = (a0 >> 26 | a1 << 4) & M26; | |||||
r->n[2] = (a1 >> 22 | a2 << 8) & M26; | |||||
r->n[3] = (a2 >> 18 | a3 << 12) & M26; | |||||
r->n[4] = (a3 >> 14 | a4 << 16) & M26; | |||||
r->n[5] = (a4 >> 10 | a5 << 20) & M26; | |||||
r->n[6] = (a5 >> 6 | a6 << 24) & M26; | |||||
r->n[7] = (a6 >> 2 ) & M26; | |||||
r->n[8] = (a6 >> 28 | a7 << 2) & M26; | |||||
r->n[9] = (a7 >> 24 | a8 << 6); | |||||
x88 = x44; | #ifdef VERIFY | ||||
for (j=0; j<44; j++) { | r->magnitude = 1; | ||||
secp256k1_fe_sqr(&x88, &x88); | r->normalized = 1; | ||||
secp256k1_fe_verify(r); | |||||
#endif | |||||
} | } | ||||
secp256k1_fe_mul(&x88, &x88, &x44); | |||||
x176 = x88; | static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a) { | ||||
for (j=0; j<88; j++) { | const uint32_t M30 = UINT32_MAX >> 2; | ||||
secp256k1_fe_sqr(&x176, &x176); | const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4], | ||||
} | a5 = a->n[5], a6 = a->n[6], a7 = a->n[7], a8 = a->n[8], a9 = a->n[9]; | ||||
secp256k1_fe_mul(&x176, &x176, &x88); | |||||
x220 = x176; | #ifdef VERIFY | ||||
for (j=0; j<44; j++) { | VERIFY_CHECK(a->normalized); | ||||
secp256k1_fe_sqr(&x220, &x220); | #endif | ||||
} | |||||
secp256k1_fe_mul(&x220, &x220, &x44); | |||||
x223 = x220; | r->v[0] = (a0 | a1 << 26) & M30; | ||||
for (j=0; j<3; j++) { | r->v[1] = (a1 >> 4 | a2 << 22) & M30; | ||||
secp256k1_fe_sqr(&x223, &x223); | r->v[2] = (a2 >> 8 | a3 << 18) & M30; | ||||
r->v[3] = (a3 >> 12 | a4 << 14) & M30; | |||||
r->v[4] = (a4 >> 16 | a5 << 10) & M30; | |||||
r->v[5] = (a5 >> 20 | a6 << 6) & M30; | |||||
r->v[6] = (a6 >> 24 | a7 << 2 | |||||
| a8 << 28) & M30; | |||||
r->v[7] = (a8 >> 2 | a9 << 24) & M30; | |||||
r->v[8] = a9 >> 6; | |||||
} | } | ||||
secp256k1_fe_mul(&x223, &x223, &x3); | |||||
/* The final result is then assembled using a sliding window over the blocks. */ | static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe = { | ||||
{{-0x3D1, -4, 0, 0, 0, 0, 0, 0, 65536}}, | |||||
0x2DDACACFL | |||||
}; | |||||
t1 = x223; | static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) { | ||||
for (j=0; j<23; j++) { | secp256k1_fe tmp; | ||||
secp256k1_fe_sqr(&t1, &t1); | secp256k1_modinv32_signed30 s; | ||||
} | |||||
secp256k1_fe_mul(&t1, &t1, &x22); | tmp = *x; | ||||
for (j=0; j<5; j++) { | secp256k1_fe_normalize(&tmp); | ||||
secp256k1_fe_sqr(&t1, &t1); | secp256k1_fe_to_signed30(&s, &tmp); | ||||
} | secp256k1_modinv32(&s, &secp256k1_const_modinfo_fe); | ||||
secp256k1_fe_mul(&t1, &t1, a); | secp256k1_fe_from_signed30(r, &s); | ||||
for (j=0; j<3; j++) { | |||||
secp256k1_fe_sqr(&t1, &t1); | VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); | ||||
} | } | ||||
secp256k1_fe_mul(&t1, &t1, &x2); | |||||
for (j=0; j<2; j++) { | static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) { | ||||
secp256k1_fe_sqr(&t1, &t1); | secp256k1_fe tmp; | ||||
} | secp256k1_modinv32_signed30 s; | ||||
secp256k1_fe_mul(r, a, &t1); | |||||
} | tmp = *x; | ||||
secp256k1_fe_normalize_var(&tmp); | |||||
secp256k1_fe_to_signed30(&s, &tmp); | |||||
secp256k1_modinv32_var(&s, &secp256k1_const_modinfo_fe); | |||||
secp256k1_fe_from_signed30(r, &s); | |||||
static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) { | VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); | ||||
#if defined(USE_FIELD_INV_BUILTIN) | |||||
secp256k1_fe_inv(r, a); | |||||
#elif defined(USE_FIELD_INV_NUM) | |||||
secp256k1_num n, m; | |||||
static const secp256k1_fe negone = SECP256K1_FE_CONST( | |||||
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, | |||||
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL | |||||
); | |||||
/* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ | |||||
static const unsigned char prime[32] = { | |||||
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, | |||||
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, | |||||
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, | |||||
0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F | |||||
}; | |||||
unsigned char b[32]; | |||||
int res; | |||||
secp256k1_fe c = *a; | |||||
secp256k1_fe_normalize_var(&c); | |||||
secp256k1_fe_get_b32(b, &c); | |||||
secp256k1_num_set_bin(&n, b, 32); | |||||
secp256k1_num_set_bin(&m, prime, 32); | |||||
secp256k1_num_mod_inverse(&n, &n, &m); | |||||
secp256k1_num_get_bin(b, 32, &n); | |||||
res = secp256k1_fe_set_b32(r, b); | |||||
(void)res; | |||||
VERIFY_CHECK(res); | |||||
/* Verify the result is the (unique) valid inverse using non-GMP code. */ | |||||
secp256k1_fe_mul(&c, &c, r); | |||||
secp256k1_fe_add(&c, &negone); | |||||
CHECK(secp256k1_fe_normalizes_to_zero_var(&c)); | |||||
#else | |||||
#error "Please select field inverse implementation" | |||||
#endif | |||||
} | } | ||||
#endif /* SECP256K1_FIELD_REPR_IMPL_H */ | #endif /* SECP256K1_FIELD_REPR_IMPL_H */ |